Determine Baseline Project Sigma and Standard Deviation

Question 1

Sigma

Answer 1

Denoted by symbol σ (a Greek alphabet) represents standard deviation of a population. Primarily it characterizes the dispersion of a set of data values with respect to mean. It refers to the mathematical concept of standard deviation.

-Sigma is a statistical term that refers to the standard deviation of a process about its mean

Question 2

Standard Deviation

Answer 2

Standard deviation is used to measure the amount of variationin a process. This is one of the most common measures of variability in a data set or population.

There are 2 types of equations: Sample and Population.

Question 3

Six Sigma

Answer 3

• Six Sigma derives from the normal or bell curve in statistics, where each interval indicates one sigma or one standard deviation. Moreover, Sigma is a statistical term that refers to the standard deviation of a process about its mean. In a normally distributed process, 99.73% of measurement will fall within ±3σ and 99.99932% will fall within ±4.5σ.
• The 68-95-99.7 rule also known as an empirical rule used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of 1, 2, and 3 standard deviations respectively.

Why would you want your baseline sigma to be 1, 2, or 3?

You would want your baseline sigma to be 1, 2, or 3 because those are indicative of bad processes and you would like your team to be able to see an improvement in the process at the end of the project.

Question 4

What is the reason behind calculating the sigma value?

Answer 4

The value in making a sigma calculation is that it abstracts your level of quality enough so that you can compare levels of quality across different fields (and different distributions.) In other words, the sigma value (or even DPMO) is a universal metric, that can help yourself with the industry benchmark/ competitors.

Question 5

How to determine baseline project sigma for discrete data

Answer 5

Calculate the process capability is through the number of defects per opportunity. The acceptable number to achieve six sigma is 3.4 Defects Per Million Opportunities (DPMO).

• Unit – the item produced or processed or created.
• Defect – anything that causes a failure (i.e. misses the customer’s requirements.)
• Opportunity – the number of critical to quality measures we are counting on each opportunity in defects. If there are 4 types of defects, this value is 4.
• DPO = Defects/(Units * Opportunity)
• DPMO =(Defects / Units * Opportunities) * Total 1,000,000
• Yield = 1-DPO (It is the ability of the process to produce defect free units).

Determine if Zero defects are needed or if there is partial credit.

• If the process is only considered correct if there are no defects at all (100% correct), then use the DPMU calculation (defects per million units) DPMU = (Defects / Units) * 1,000,000
  
  • If partial credit is received for meeting some of the requirements: use the DPMO calculation (defects per million opportunities) DPMO = (Defects / Units * Opportunities) * Total 1,000,000

Question 6

Examples of Baseline Sigma for Discrete Data

Answer 6

Example: XYZ is a commercial flight carrier operating 10,000 flights a day. There are three defect opportunities like late arrival, lost luggage and poor in-flight experience. Let’s assume 10,000 defects identified. Calculate process sigma level.

• Unit or sample size = 10,000 flights a day
• Defects types = 3 (could be late arrival, lost luggage, poor in-flight experience).
• Opportunities = 10,000 flights * 3 kinds of defect opportunities = 30,000
• Defects: 10,000 defects
• DPMO = (Defects / Units * Opportunities) * 1,000,000
• DPMO= (10000 /10000*3) * 1,000,000 = (1/3) * 1M. = 333,333 defects per Million opportunities.
• From the below chart, 333,333 DPMO translates to a sigma between 1.95 and 1.9.

Question 7

How to Determine Baseline Project Sigma for continuous data

Answer 7

Process Capability is the determination of the adequacy of the process with respect to the customer needs. Process capability compares the output of an in-control process to the specification limits. We can say the process is capable when almost all the measurements fall within the specification limits. Cp and Cpk are considered short-term potential capability measures for a process.

Question 8

Cpk

Answer 8

Cpk is a measure to show how many standard deviations the specification limits are from the center of the process.

• C_plower = (Process Mean – LSL)/(3*Standard Deviation)
• C_pupper = (USL – Process Mean)/(3*Standard Deviation)
• Cpk is smallest value of the Cpl or Cpu: C_pk= Min (C_pl, C_pu)

The main purpose of C_pk is to determine how close a process is performing when compared to its specification limits and considering the natural variability of the process. Always larger Cpk is better, it indicates the less probability of any item will be outside the specification limits.

Process sigma = 3* C_pk. Hence We generally want a C_pk of at least 1.33 [4 sigma] or higher to satisfy most customers.